Depends on the tow truck, IMO. The longer the bed extends, the less angle it makes with the ground and the less likely the car is to drag.
The problem is not just how high the car is in the back, but how far the body extends behind the rear axle. Your van sticks out a lot more than the TR3! My Stag was about equally likely to drag bottom in my driveway as the TR (before I lowered the TR), and it had no trouble going onto the flatbed that AAA sent out a few years back.
The 3'9" figures quoted above are the "track", meaning center of tire to center of tire. The actual clearance between the sidewalls is somewhat less. With stock rims & tires, it's probably only 39" sidewall-to-sidewall ... which will still fit fine on that 35" ramp if you are careful to line the car up perfectly. I've even done it with part of the tire hanging out in space, but of course that requires even more care to be sure it's perfectly lined up and stays that way.